"She is a long and sleek ship with an engine housing twice as large as that of a normal ship its size." As a ship's boat, the Razorback would have a length of 20-30 meters. It has engines that have been optimized for racing and likely has minimal mass and thus minimal equipment in order to maximize speed and maneuverability. The engine compartment is sealed and inaccessible from within the ship.
After Julie left Earth and Luna for Ceres Station and joined the OPA, the Razorback remained there, docked at her father's space station in Earth's L1. Her parents threatened to sell the boat in an unsuccessful ploy to coerce Julie to return to them.
When Julie was assimilated into the protomolecule life-form on Eros during the Eros incident, the life-form experimented with the station's PA system, forming incoherent sentences thought to have been taken from the computer system's data banks. When it repeatedly shouted "You can't take the Razorback!", however, Miller realized that Julie's mind was at the center of the protomolecule hybrid life-form.
When Chrisjen Avasarala and Bobbie Draper were taken prisoner aboard the Guanshiyin, the yacht of Julie's father Jules-Pierre Mao, they found the Razorback in one of its shuttle bays and escaped in it. It takes them to meet the Rocinante. From there, Jim Holden uses it go make the trip to and away from the Agatha King while the Rocinante proceeds to the surface of Ganymede.
The Razorback ended up in UN hands. When Avasarala employed Bobbie again, the politician gave her the ship as a payment for favors. Bobbie and Alex Kamal used it to travel to the Hungaria group of asteroids to investigate for Jim Holden.